Bullet and Snell's law?

[michel123456]

1.When you shoot a ball against a wall, the object hits the wall and eventually rebounds following the laws of physics: if the wall is made of a perfect surface, the angle of incidence is the same as the angle of reflection. It is the same law that applies for waves.

 

2. When you shoot a bullet through a liquid (like shooting with a gun into a pound of water), will the bullet follow a path according to Snell"s law? Will the angle change when the bullet is in water?

Edited April 18, 2014 by michel123456

[swansont]

Under many circumstances, yes. The part of the bullet that first strikes the water will slow down, while the rest of it wants to proceed at the speed it was traveling at. So there will be a torque that tends to turn it.

[michel123456]

Under many circumstances, yes. The part of the bullet that first strikes the water will slow down, while the rest of it wants to proceed at the speed it was traveling at. So there will be a torque that tends to turn it.

(emphasizing mine)

 

Isn't that enough to put Snell's law at work?

I mean, the slowing down of the bullet.

[Enthalpy]

Letting the bullet spin doesn't suffice to deflect it. And from asymmetric force perpedicular to the initial speed, I'd rather expect a small deflection towrds the air.

 

Head-on against a wall, the bullet or the wall is squeezed, or both. The rebound, if any, is weak. The best materials achieve a head-on elastic rebound at 40m/s or little more, while rifle bullets can have 300-800m/s and aren't hard neither.

 

Computer simulations of a bullet impact, or a kinetic impactor (often >800m/s), use to neglect completely the strength of the bullet, and model it as a liquid with inertia.

[rktpro]

(emphasizing mine)

 

Isn't that enough to put Snell's law at work?

I mean, the slowing down of the bullet.

The origin of Snell's Law is Fermat's Principal of least time. For a mechanical object like bullet, I think swansont correctly mentions torque to play a role.

[michel123456]

The origin of Snell's Law is Fermat's Principal of least time. For a mechanical object like bullet, I think swansont correctly mentions torque to play a role.

Yes, that could be a rephrasing of my question:

Does the Fermat's principle apply to mechanical objects? Or only to waves?

[John Cuthber]

Snell's law refers to the refractive index.

That, in turn is the ratio of the two characteristic velocities.

But a bullet in water or air doesn't have a characteristic velocity so no, Snell's law doesn't apply.

Try Newton's laws.

[rktpro]

Indeed Snell's law applies to waves only. It is backed by Hyugen's principal, which works for waves.

[michel123456]

Snell's law refers to the refractive index.

That, in turn is the ratio of the two characteristic velocities.

But a bullet in water or air doesn't have a characteristic velocity so no, Snell's law doesn't apply.

Try Newton's laws.

I don't understand.

 

A bullet in air has velocity V1

Getting in water, it has velocity V2<V1

 

i understand that V1 is not an intrinsic characteristic of the bullet, nor a characteristic of the air. The same for V2.

However, there exist a ratio V1,V2 which is characteristic of this particular bullet.

And if there is such a ratio, why does the bullet continue on a sraight path, or not?

 

Also I understand that Snell's law applies relatively to the angle to the surface.

IOW the question is: does the surface of the liquid produce some force, oriented as a vector that it is, in some direction that is not the same as the incident path of the bullet. Because if there is such a force, then the path of the bullet is modified.

If this force, which I think does exist, is a function of V1 and V2, then we are not far from Snell's law.

Edited April 19, 2014 by michel123456

[swansont]

(emphasizing mine)

 

Isn't that enough to put Snell's law at work?

I mean, the slowing down of the bullet.

 

It's enough to say the angle will change and pull the bullet away from the normal, as asked in the OP, but strictly following Snell's law requires more conditions to be met, as other have pointed out. I think it's fair to say that there will be a tendency to qualitatively follow Snell's law.

[John Cuthber]

When the front end of the bullet hits the water it has one velocity.

When the back end of the bullet reaches the water, it has a different velocity.

Which one do you think is "in water, it has velocity V2"?

Obviously, there's a force which acts on the bullet, but the similarity to refraction is pretty slight.

Among other issues, it depends on the shape of the bullet.

Where is that factor in Snell's law?

[michel123456]

I mean this below diagram holds also for a stone you throw at a pond of water (like stone skipping). It is not so specific to waves.

 

[John Cuthber]

How might you hope to define n?

The speed keeps changing with distance.

 

(And that illustration is wrong- for the critical angle the path is along the surface of the interface. Let's see you get a bullet to do that.)

[michel123456]

This below is better?

 

 

If one replaces the water surface with unbreakable steel, the bullet would rebound (if not melted by the impact) along a direction with same angle Θ incident. Since it is water and not steel, the bullet goes through the surface but there must be some tiny repelling force at angle Θ as indicated on the diagram. The decomposition of vectors must in this case show that the path of the bullet slightly changes. This is totally independent of the shape of the bullet, or whether the head of the bullet hits first while the rest of the bullet hits afterwards.

 

[swansont]

In both ricochet and penetration, the angles would probably not be the same as they are in optics.

[michel123456]

In both ricochet and penetration, the angles would probably not be the same as they are in optics.

Sure.

But the mathematics would be equivalent. i mean with other values but according to a similar equation.

I guess.

Or to say it differently: I suspect there should be a generalizing equation that is valid for both optics and for material objects. With a M value for mass, when M=0 then you get Snell's law. Or something like that.

Edited April 19, 2014 by michel123456

[swansont]

Sure.

But the mathematics would be equivalent. i mean with other values but according to a similar equation.

I guess.

Or to say it differently: I suspect there should be a generalizing equation that is valid for both optics and for material objects. With a M value for mass, when M=0 then you get Snell's law. Or something like that.

 

Properties of the bullet other than mass probably play a role. How soft the material is, for example.

[J.C.MacSwell]

 

Properties of the bullet other than mass probably play a role. How soft the material is, for example.

As well as mass?

 

The path would be effected by the mass of the bullet, given that other things being equal at any given point, the forces on the bullet would be identical (at that point). So a heavier bullet would respond differently than a lighter one, which would effect the forces going forward etc.

 

Generally speaking there would be increased drag as it met the surface, which would rotate it but not initially pull it under (and some lift which might counter that rotation), depending on the shape and centre of gravity. With enough downward momentum it will break the surface, and the rotation would give it an angle of attack that would cause the refraction downward (or not if rotated upward). Without enough downward momentum to break the surface it would generally bounce/skip due to the lift.

 

So I don't believe a generalized equation will work, unless it is a very complicated one.

Edited April 20, 2014 by J.C.MacSwell

[swansont]

As well as mass?

 

Yes, of course. Michel limited the example to mass, and that's not going to work.